PINCHING THEOREMS FOR TOTALLY REAL MINIMAL SUBMANIFOLDS INCPn

Abstract

AbstractLetMbe ann-dimensional totally real minimal submanifold inCPn. We prove that ifMis semi-parallel and the scalar curvature τ,$\frac{-(n-1)(n-2)(n+1)}{2}\leq \tau \leq 0$, thenMis an open part of the Clifford torusTn⊂CPn. IfMis semi-parallel and the scalar curvature τ,$n(n-1)\leq \tau \leq \frac{n^{3}-3n+2}{2}$, thenMis an open part of the real projective spaceRPn.